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We will rotate each vertex and then connect the images. Let's start by rotating $A.$ To do so, we will draw $\overline{AO}$ and then construct $\overline{A'O}$ such that the segments are congruent and perpendicular.
By repeating the process with $B$ and $C,$ we can obtain their images $B'$ and $C'.$ Then, we connect $A',$ $B',$ and $C'$ to draw the image of the given triangle.